Related papers: On generalized Stone's Theorem

It has been a longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a nonseparable counterexample. The existence of a separable counterexample remains an open…

In this article, we give a general construction of spectral triples from certain Lie group actions on unital C*-algebras. If the group G is compact and the action is ergodic, we actually obtain a real and finitely summable spectral triple…

Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…

We define the profinite completion of a C*-algebra, which is a pro-C*-algebra, as well as the pro-C*-algebra of a profinite group. We show that the continuous representations of the pro-C*-algebra of a profinite group correspond to the…

We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…

We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

We prove constructive versions of various usual results related to the Gelfand duality. Namely, that the constructive Gelfand duality extend to a duality between commutative nonunital C*-algebras and locally compact completely regular…

We construct a unital pre-C*-algebra $A_0$ which is stably finite, in the sense that every left invertible square matrix over $A_0$ is right invertible, while the C*-completion of $A_0$ contains a non-unitary isometry, and so it is…

In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…

Let $G$ be a locally compact group and $P \subset G$ be a closed Ore semigroup containing the identity element. Let $V: P \to B(\clh)$ be a representation such that for every $a \in P$, $V_{a}$ is an isometry and the final projections of…

We propose a definition of a "$C^*$-Eberlein" algebra, which is a weak form of a $C^*$-bialgebra with a sort of "unitary generator". Our definition is motivated to ensure that commutative examples arise exactly from semigroups of…

We describe representations of groupoid C*-algebras on Hilbert modules over arbitrary C*-algebras by a universal property. For Hilbert space representations, our universal property is equivalent to Renault's Integration-Disintegration…

Let $\M=P\times{M}$ be a variable Mautner group. We describe the $C^*$-algebra $C^*(\M)$ of $\M$ in terms of an algebra of operator fields defined over $P\times{\C^2} $.

We provide a complete description of the order isomorphisms between the self-adjoint parts of $C^*$-algebras. Furthermore, we characterize such isomorphisms between general operator intervals in $AW^*$-algebras. For the description, we use…

For a smooth manifold with boundary we construct a semigroupoid and a continuous field of C*-algebras which extend Connes' construction of the tangent groupoid. We show the asymptotic multiplicativity of \hbar-scaled truncated…

We give an explicit injective representation of the universal $\mathrm{C}^\ast$-algebra that is generated by doubly non-commuting isometries. This injectivity allows us to prove that such universal algebras embed naturally into each other…

We investigate conditions on a graph $C^*$-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth $(1,\infty)$-summable semfinite…

We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable…

We introduce the notion of a (noncommutative) C*-Segal algebra as a Banach algebra which is a dense ideal in a C*-algebra. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of…

In this paper, we introduce a new technique in the study of the $*$-regular closure of some specific group algebras $KG$ inside $\mathcal{U}(G)$, the $*$-algebra of unbounded operators affiliated to the group von Neumann algebra…